metrology, Roman
metrology, Roman
- Andrew M. Riggsby
Summary
There is a large body of evidence for Roman use of weights and measures. In theory, they would have been able to measure a variety of quantities with great precision, given the variety of different-sized units at their disposal and an elaborate system of fractional subdivisions of those units. Moreover, those measurements could have been accurate with respect to a shared system because of publicly available exemplary standards, a theoretical connection between the definitions of the most important measurements, and the existence of state officials who could enforce the standards. As a result, Romans could, in principle, have conveyed very specific metrological information across a great deal of space and time. In practice, measurement was considerably less predictable and less precise. Actual measurement did not necessarily avail itself of the full resources of the theoretical system, and sometimes did not appeal to any general system. Moreover, overtly competing systems coexisted with the “official” ones at all times. Finally, it is not clear how coherent that official system was, nor were the actual systems of enforcement particularly robust. As a result, measurement was often imprecise and/or tightly localized (which probably generated weak expectations of being able to replicate measurement across different contexts).
Subjects
- Ancient Economy
- Science, Technology, and Medicine
- Roman History and Historiography
Approaches to Measurement
An enormous quantity of equipment for weighing survives: balance scales and both labelled and unlabelled weights (see Figure 1). We also have significant numbers of rulers and sundials (see Figures 2 and 3 respectively), plus a few volumetric measuring vessels (though many unlabelled vessels could also have been used for measurement). Both epigraphic evidence and surviving treatises testify extensively to the work of land surveyors (see gromatici). We also have more scattered, but still extensive textual evidence for the wide employment of professional measurers (mensores) of other sorts, as in the grain, oil, and building trades. The numbers and specialization of these tradesmen illustrate the importance of measurement (as a practice), but perhaps also reveal a lack of confidence in the results of measurements detached from their original social context.
Figure 1. Roman steelyard balance with weight.
Figure 2. Roman compass-style ruler.
Still, measurement did not always make reference to the kinds of generalized standards notionally available.1 Recipes (both culinary and pharmaceutical) are sometimes framed in dimensionless proportions (e.g., “one part of this, two parts of that”). Others use more concrete units (coins as weights, cups as volumes), but ones that are not precisely standardized, and are so essentially proportional as well. In that light, it is possible to read even directions which notionally refer to a standardized unit as proportional as well, as long as (and this is common) there is only reference to a single unit. Theoretical architectural design depended heavily on ratios rather than specific measurements. There is also evidence for the importance of proportion in actual construction as well, measuring physical elements directly against each other or against a local, purpose-built device (e.g., a sketch or model) rather than relying on generalized measuring devices (e.g., different rulers).
For any given quantity to be measured, the Roman system provided multiple base units (two for weight, more for the others; see “Specific Measurements”). They also had a well-developed system of named fractions, centred on twelfths. In principle, these could be combined to measure even very large quantities with great precision, but in practice such combinations (either of different units or of compound fractions) were rare.
As in many other societies with limited literacy, Romans’ recorded ages are frequently rounded to the nearest 5 or 10.2 In that case we can assume what the distribution of the actual figures should have been, but it is rare that we can directly measure Roman tolerance for approximation and rounding in other contexts. Still, particular circumstances sometimes allow us to detect approximations even in legal documents and state bureaucratic records. Moreover, we can statistically detect a preference for stereotypical figures even in leading digits (e.g., 400, 4000, 40000) in at least some contexts.3 In short, using the form of a specific numerical measurement did not necessarily promise the reader any particular degree of precision.
Regulation
The first known legal regulation of weights and measures is the lex Silia of probably the mid-3rd century bce (Festus, Gloss. Lat. 288).4 This statute standardized several customary volumetric measures in terms of certain weights of wine, and punished magistrates who produced official exemplars not conforming to these definitions. Subsequent public law similarly focuses on protecting the integrity of public standards. It is only in the late 4th century ce that we see attempts by the central state to promulgate (physical) standards widely or to compel their use.
Below the level of the central state, there are more significant efforts at standardization, but often with local intention or effect.5 There were officials (esp. Roman aediles and Greek agoranomoi) with jurisdiction over particular marketplaces. They could forbid use of particular scales or containers, and sometimes even destroyed them in theatrical fashion. More positively, local elites would from time to time give full or partial sets of standards to local markets as a form of euergetism. And individuals could in principle sue business partners for use of improper weights or measures. In all these cases, however, there is essentially no evidence for connection to the standards of Rome.
In fact, considerable evidence suggests the ongoing existence of deliberate metrological diversity. We have measuring devices, both private and apparently public, which can be used to measure in a variety of different systems (for example, an inscribed table with markings for Roman feet, Punic cubits, and Egyptian cubits or steelyards that can be hung to measure in multiple different units). Weights have been found at multiple sites issued by Roman authorities but explicitly calibrated to indigenous standards.6 As a general matter, the law permitted transactions defined not just by local standards, but by any that the parties agreed to (Papin. dig. 18.1.71; cf. Paul. dig. 4.3.18.3).
Over time, learned experts developed an elaborate set of equivalences between Roman units of measure (and to some extent extended their reach to “foreign” systems), and much of this could have held good in practice.7 However, systemization required ignoring competing definitions of some units, especially the smallest and largest ones, but also centrally important ones (see “Volume” on the various modii).
Reconstruction
There is a long tradition of antiquarian efforts to reconstruct the value of Roman units of measure in modern terms.8 For units of weight this is typically done by direct measurement of labelled weights surviving from antiquity; the most influential studies, however, are based on gold coinage which (on average) should correspond to a known fraction of the pound and over which great care was likely taken by the authorities at the mint. For length we have a very small number of official-seeming standards, plus a larger number of purpose-built rulers owned by individuals. Scholars have also inferred values of the foot by measuring large buildings (whose design seems typically to have relied on simple numerical multiples of some “module,” that is a basic measurement).9 Only a very small number of labelled volumetric measures survive intact, so results from those are typically combined with theoretical weight equivalents (based on the lex Silia; see “Regulation”) to arrive at approximate values. The units of time all have familiar astronomical references (the day, the year, etc.) and are well understood, which allows assessment of accuracy and likely place of manufacture.10
Most studies assume that there is a single “true” value for each of the measures. There are some general reasons to doubt this assumption (see “Approaches to Measurement” and “Regulation”). This undercuts specific conclusions that rely on high precision (e.g., supposed continuity of measures across cultures on the one hand or finely detailed chronology of supposed evolution of standards on the other). Still, the basic values derived for the various units (see “Specific Measurements”) seem meaningful and sound. Additionally, it can be noted that attempts at diachronic studies have sometimes detected reduction in the value of the pound and the foot. Larger weights and measures are typically more uniform than smaller ones, and there is a rough hierarchy in which measures for length are more uniform than those for weight, which are in turn more uniform than those for volume. (Note that containers from the wholesale trade in olive oil show it was sold by weight.)
Specific Measurements
Equivalents in modern units given in this section are provided to suggest an order of magnitude and are not meant to render judgement on scholarly disputes over these questions.
Weight
The named units were the libra (“pound”; 325 g (12 oz)) and the uncia (“ounce”; literally “1/12” so about 27 g (1 oz)). Several sites are attested as housing official weight standards, and we even have dozens of weights whose label claims calibration to a standard housed at the Temple of Castor in the Roman Forum.11 Most labelled weights fall within several per cent of “expected” weight, but deviate from that expectation more than would be unavoidable given the technology used to construct them and at any rate to a degree readily detectable at the time. More dramatic outliers (e.g., a 20 per cent deviation) are not hard to find. It has also been suggested that the official weight standards were not all exactly equal to one another, though the evidence is inconclusive.
Time
Long periods of time were reckoned by counting days, months, and years in essentially the same way as today (see calendar, Roman). Shorter periods were measured in two different ways for two different purposes.12 Durations were measured by water clocks. These seem not necessarily to have been calibrated to any larger system; rather, their purpose was to maintain proportions in some local context, most notably the time allotted to speakers in court. The time at which some event should happen was typically fixed in terms of hours (horae) of the day, as shown by a sundial at or near the event in question (see Figure 3). There were twelve of these hours, spaced evenly throughout the time from sunrise to sunset. Neither sundials nor water clocks seem to have been used normally to synchronize events at different locations, and even clocks in the same vicinity notoriously disagreed with each other.
Figure 3. Roman Sundial, 2nd century ce.
It is commonly said that the hour (in the sense of 1/12 of the day) at Rome varied across the seasons from 45 to 75 minutes. This is true, but it should be noted that such “hours” were not in fact principally measures of duration. The systems for timing and duration were occasionally synchronized, but this seems only to have happened in technical contexts (in particular astronomers made use of a standardized “aequinoctial” hour, essentially 60 of our minutes).
Length
Length was measured, according to context, in a wide variety of units: principally the pes (“foot”; just short of 300 mm (12 in.)), competing subdivisions (the uncia and digitus, 1/12 and 1/16 of the pes, respectively), the cubitus (440 mm (17 in.)), passus (“pace”; almost 1.5 m (5 ft)), and the Roman “mile” (milia [passuum]; 1.5 km (1 m)). Scale is clearly the most important discriminant, but there are others. For instance, cubits are common in discussion of cultures where they (rather than versions of the foot) are the conventional small measure; paces seem largely limited to contexts of approximation.
Formal land surveying used the same units, but also added a few of its own (e.g., the pertica of 10 feet), but is perhaps most notable for using feet even over long distances.13 The surveyors also used a number of units of land area ranging from the scrupulum (10 m2 (105 ft2)) to the centuria (50 ha (125 acres)). Unusually, a measurement once made by a land surveyor appears to have binding legal value not just in its immediate context, but in any future dispute.
Volume
Volume was also measured by a large variety of units, ranging from the cyathus (40 ml (3 Tbs.)) to the sextarius (500 ml (1 pt)), and from there up to the modius (9 l (16 pts); dry capacity) or the amphora (25 l (45 pts); liquid). Modius etymologically means just “measure(ment)” (see Figure 4), and in fact the same name was given to at least five different standards (similar homonymy affects other measures to a lesser degree).14
Figure 4. Roman coin showing the characteristic form of a modius grain measure, 41 ce.
Several dozen volumetric measuring tables (large stone slabs with conical or hemispherical cavities on the upper surface and sometimes a seeming “drain” through the bottom of the table; see Figure 5) survive, but they present numerous difficulties of interpretation.15 Almost none of our surviving tables carries any labels indicating the intended capacity of the cavities. Measured capacities of these cavities occasionally correspond to expected values of standard units, but that is more often not the case. Finally, we do not even really know how the devices were used, for instance, whether the cavities were sometimes filled directly or whether (very rarely attested) metal liners were always used or why only some cavities have the drains.
Figure 5. Measuring table from Pompeii, 1st century bce (text CIL 10.783).
Bibliography
- Berrendonner, Clara. “La Surveillance des poids et mesures par les autorités romaines: l’apport de la documentation épigraphique latine.” Cahiers du Centre Gustave Glotz 20 (2009): 351–370.
- Cioffi, Carla. “Documenting, Measuring and Integrating sekomata: An Example from Naxos.” Dialogues d’histoire ancienne, Suppl. 12 (2014): 41–56.
- Cloud, John. “A ‘Lex De Ponderibus’ (Festus p. 228 L).” Athenaeum 63 (1985): 405–418.
- Corti, Carla, and Nicoletta Giordani. Pondera: pesi e misure nell’antichità. Campogalliano, Italy: Museo della bilancia, 2001.
- Cuomo, Serafina. “Measures for an Emperor: Volusius Maecianus’ Monetary Pamphlet for Marcus Aurelius.” In Ordering Knowledge in the Roman Empire. Edited by Jason König and Tim Whitmarsh, 206–226. Cambridge, UK: Cambridge University Press, 2007.
- Duncan-Jones, Richard. “The Choenix, the Artaba and the Modius.” ZPE 21 (1976): 43–52. Duncan-Jones’ contributions to this area of study are enormous, but largely scattered through numerous individual articles and chapters. I cite only the papers most directly connected to the material in this article.
- Duncan-Jones, Richard. “Age-Rounding, Illiteracy, and Social Differentiation in the Roman Empire.” Chiron 7 (1977): 333–353.
- Gibbs, Sharon. Greek and Roman Sundials. New Haven, CT: Yale University Press, 1976.
- Haensch, Rudolf, and Peter Weiss. “Ein weiteres ‘Statthaltergewicht’ von Nikomedeia: Neue Ergebnisse zur Stadt- und Reichsgeschichte.” Chiron 44 (2014): 513–549. This article is the culmination of a series of studies, many by Weiss alone or in other combinations, on this important set of evidence.
- Hultsch, Friedrich. Metrologicorum scriptorum Reliquiae. Vols. 1–2. Leipzig: Teubner, 1864.
- Lange, Margret. “Mensae ponderariae in Italien: Versuch einer Bestandsaufnahme und Analyse.” PhD Diss., Westfälische Wilhelms University, 2010.
- Luciani, Franco, and Tomaso Lucchelli. “Pondera exacta ad Castoris.” In Instrumenta inscripta VI: Le iscrizioni con funzione didascalico-esplicativa. Edited by Maurizio Buora and Stefano Magnani, 265–289. Trieste, Italy: Editreg, 2016.
- Riggsby, Andrew. Mosaics of Knowledge: Representing Information in the Roman World. Oxford: Oxford University Press, 2019.
- Saliou, Catherine. “Introduction.” In Dialogues d’histoire ancienne. Supplément n°12. La Mesure et ses usages dans l’antiquité. Edited by Catherin Saliou, 9–16. 2014.
Notes
1. Andrew Riggsby, Mosaics of Knowledge: Representing Information in the Roman World (Oxford: Oxford University Press, 2019), 85–100.
2. Richard Duncan-Jones, “Age-Rounding, Illiteracy, and Social Differentiation in the Roman Empire,” Chiron 7 (1977): 333–353.
3. Walter Scheidel, “Benford’s Law and Numerical Stylization of Monetary Valuations in Classical Literature,” CQ 66 (2016): 815–821 and Riggsby, Mosaics of Knowledge, 84–5, 98–100.
4. John Cloud, “A ‘Lex De Ponderibus’ (Festus p. 228 L),” Athenaeum 63 (1985): 405–418.
5. Riggsby, Mosaics of Knowledge, 100–120; Clara Berrendonner, “La Surveillance des poids et mesures par les autorités romaines: l’apport de la documentation épigraphique latine,” Cahiers du Centre Gustave Glotz 20 (2009): 351–370. Antonio D.Pérez Zurita, “Control y administración de pesos y medidas en las ciudades del Imperio romano (‘Pars Occidentalis’),” Gerión 29, no. 1 (2011): 123–148; and Alain Bresson, The Making of the Ancient Greek Economy: Institutions, Markets, and Growth in the City-States (Princeton, NJ: Princeton University Press, 2016), 239–242.
6. Rudolf Haensch and Peter Weiss, “Ein weiteres ‘Statthaltergewicht’ von Nikomedeia: Neue Ergebnisse zur Stadt- und Reichsgeschichte,” Chiron 44 (2014): 513–549, which sums up considerable work by the authors and collaborators.
7. Serafina Cuomo, “Measures for an Emperor: Volusius Maecianus Monetary Pamplet for Marcus Aurelius,” in Ordering Knowledge in the Roman Empire, ed. Jason König and Tim Whitmarsh (Cambridge, UK: Cambridge University Press, 2007), 206–226. For the primary texts, see Friedrich Hultsch, Griechische und römische Metrologie (Berlin: Weidmannsche Buchhandlung, 1882).
8. Hultsch, Griechische und römische Metrologie. For more recent reviews, though perhaps not adding much clarity, see Konrad Hecht, “Zum römischen Fuss,” Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft 30 (1979): 107–137 and Richard Duncan-Jones, Money and Government in the Roman Empire (Cambridge: Cambridge University Press, 1994), 213–215.
9. Hecht, “Zum römischen Fuss.”
10. Sharon Gibbs, Greek and Roman Sundials (New Haven, CT: Yale University Press, 1976). There is also much of general interest on the topic in the notionally more specialized study of Richard J. A. Talbert, Roman Portable Sundials: The Empire in Your Hand (Oxford and New York: Oxford University Press, 2017).
11. Franco Luciani and Tomaso Lucchelli,“Pondera exacta ad Castoris,” in Instrumenta inscripta VI: Le iscrizioni con funzione didascalico-esplicativa, ed. Maurizio Buora and Stefano Magnani (Trieste, Italy: Editreg, 2016), 265–289.
12. Kevin K. Birth, “The Vindolanda Timepiece: Time and Calendar Reckoning in Roman Britain,” Oxford Journal of Archaeology 33, no. 3 (2014): 395–411.
13. Brian Campbell, ed., The Writings of the Roman Land Surveyors: Introduction, Text, Translation and Commentary. Journal of Roman Studies. Monographs 9 (London: Society for the Promotion of Roman Studies, 2000).
14. Richard Duncan-Jones, “The Choenix, the Artaba and the Modius,” ZPE 21 (1976): 43–52.
15. Margret Lange, “Mensae ponderariae in Italien: Versuch einer Bestandsaufnahme und Analyse” (PhD Diss., Westfälische Wilhelms University, 2010); and Carla Cioffi, “Documenting, Measuring and Integrating sekomata: An Example from Naxos,” Dialogues d’histoire ancienne, Suppl. 12 (2014): 41–56. It is hoped that Cioffi will eventually publish a synthetic work on eastern measures comparable to Lange’s for the west.
